Here is the link. keywords: [exponential sensitivity to small perturbations] [exponential sensitivity to initial conditions] [diverse functional roles in living systems] [detecting chaos from empirical measurements] [sensitivity to measurement noise] [difficult edge-cases] [varying degrees of chaos] [noisy recordings] [to denoise the inputted signal] [Schreiber’s noise-reduction algorithm] [Chaos Decision Tree Algorithm] [Matlab code freely and publicly … Continue reading article: A simple method for detecting chaos in nature

# Day: January 21, 2021

# article: Extremely simple nonlinear noise-reduction method

(Schreiber’s noise-reduction algorithm) Here is the link. keywords: [experimental data] [nonlinear time evolution] [locally constant fits] [a less noisy trajectory] [coordinates from the past and from the future] [Hénon map] [Mackey-Glass equations]

# Mackey-Glass equations

Here is the link to the Wikipedia article on this topic. “There exist an enormous number of physiological systems that involve or rely on the periodic behavior of certain subcomponents of the system.” keywords: [mathematics] [mathematical biology] [delay differential equations] [to mimic both healthy and pathological behavior] [relative quantity of mature cells in the blood] [chaotic attractors]

# the Hénon map

Here is the link to the Wolfram MathWorld article on this topic. (I’m not linking to the Wikipedia article on this topic, because the Wikipedia article on this topic contains an error.) keywords: [two-dimensional dissipative quadratic map] [coupled equations] [quadratic area-preserving map] [one of the simplest two-dimensional invertible maps]

# form entailed by even perfect numbers

form entailed by even perfect numbers keywords: [Mathematics] [Number Theory] [Proof Theory] [Logic] [X + Y = X implies Y = 0] [sum-of-divisors function] [multiplicative function]

# the 5 Bodean authors

Bode’s law posits constant proportionality of distance from the Sun for the planets. It’s only approximately true, but let’s take the idea and run with it in a different domain: author popularity, for authors of fiction. Bode’s law works from close to far, but we will apply the concept starting at the greatest distance in … Continue reading the 5 Bodean authors